CBSE Class 12-science Answered

With the help of a neat and labeled diagram, explain the underlying principle and working of a moving coil galvanometer. What is the function of: (i) uniform radial field (ii) soft iron core in such a device? OR Derive a mathematical expression for the force per unit length experienced by each of the two long current carrying conductors placed parallel to each other in air. Hence define one ampere of current. Explain why two parallel straight conductors carrying current in the opposite direction kept near each other in air repel?

Asked by Topperlearning User | 21 May, 2015, 12:55: PM

Expert Answer

(a) Moving coil galvanometer

Principle: A current carrying coil suspended in a magnetic field experiences a torque.

Working: When current is passed say long ABCD, the couple acts on it. AB experiences outward force and CD, the inward force in accordance with Fleming's left hand rule. Since the plane remains always parallel to the magnetic field in all position of the coil (radial field), the forced on the vertical arms always remains perpendicular to the plane of the coil.

Let I = the current flowing through coil.

B = magnetic field supposed to be uniform and always parallel to the coil.

l = length of the coil

b = breadth of the coil

N = no. of turns in the coil

Deflecting torque acting on the coil is

where A = lb = area of the coil.

Due to deflecting torque, the coil rotates and suspension wire gets twisted. A restoring torque is set up in the suspension wire. If is angle through which the coil rotates and k is the restoring torque per unit angular twist, then Restoring torque,

In equilibrium,

Defecting torque = Restoring torque

NIBA = k

Where G = k/NBA, is the galvanometer constant.

This provides a linear scale for the galvanometer.

(b) Function of uniform radial magnetic field: Due to radial magnetic field, sin=1 in the expression for torque. This makes the deflection proportional to current, i.e. it makes the scale linear.

Function of soft iron core: To produce radial magnetic field pole pieces of permanent magnet are made cylindrical and a soft iron core is placed between them. The soft iron core helps in making the field radial and reduces energy losses produced due to eddy currents.

Consider two infinitely long thin conductors carrying current in opposite directions. Magnetic field B₁ due to I₁at P on 2^nd conductor is given by

The magnetic field B₁ is perpendicular to plane of paper and directed inward. This field will produce a force/length F₂ and 2^nd conductor given by

By Fleming's left hand rule direction of F₂ is away from 1^st conductor.

Similar the current I₂ will create a field B₂ at Q directed inward which is turn will create force/lengthv F₁

By Fleming's left hand rule, the direction of F₁ is away from the second conductor. Hence the two conductors repel each other.

Ampere.

If I₁ = I₂ = IA, and r = Im, then

Thus one ampere is that current which on flowing through each of the two parallel uniform linear conductors placed in free space at a distance of one meter from each other produces between them a force of 2 10^-7 N per meter of their lengths.